Victoria Grushkovskaya, Sameh Eisa · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27239 · open-access PDF
이 논문에서 우리는 최근에 개발 된 일반 높은 순서의 Lie 브래켓 접근 이론과 제어 친화적 인 시스템의 프레임 워크를 활용하여 (i) 사각형 객체 기능에 대한 계수적 접근 비율과 비 사각형 객체 기능에 대한 폴리노미 접근 비율을 제공하는 첫 번째 순서의 Lie 브래켓 접근 (first-order Lie bracket approximation), 그리고 (ii) 최소화기 근처의 계수적 접근 비율을 제공하는 높은 순서의 Lie 브래켓 접근 (high-order Lie bracket approximation)을 설계 할 수 있음을 보여줍니다.
Machine translation (Meta M2M100); the English original follows.
In this paper, we leverage the recently developed general higher-order Lie bracket approximation theory and framework for control-affine systems to show that we can design extremum seeking (ES) systems that combine flows based on: (i) first-order Lie bracket approximation, which provide an exponential convergence rate for quadratic objective functions and polynomial convergence rate for non-quadratic objective functions; and (ii) higher-order Lie bracket approximation, which provide exponential convergence rate near the minimizer even if the objective function is non-quadratic (i.e., flatter a
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